Transportation Research Part C 45 (2014) 83–98

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Transportation Research Part C

journal homepage: www.elsevier .com/locate / t rc

Multi-agent simulation of individual mobility behaviorin carpooling

0968-090X/$ - see front matter � 2014 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.trc.2013.12.012

1 http://www.multiagent.fr.2 http://www.uhasselt.be/imob.⇑ Corresponding author. Tel.: +33384583418; fax: +33384583342.

E-mail address: stephane.galland@utbm.fr (S. Galland).

Stéphane Galland a,⇑, Luk Knapen b, Ansar-Ul-Haque Yasar b, Nicolas Gaud a, Davy Janssens b,Olivier Lamotte a, Abderrafiaa Koukam a, Geert Wets b

a Multiagent Group, IRTES-SET, UTBM, 90010 Belfort Cedex, France1

b Transportation Research Institute (IMOB), Hasselt University, Wetenschapspark 5 bus 6, 3590 Diepenbeek, Belgium2

a r t i c l e i n f o

Article history:Received 14 May 2013Received in revised form 8 November 2013Accepted 31 December 2013Available online 22 January 2014

Keywords:Carpooling problemMulti-agent simulationOrganizational modelJanus platformJaSim environment modelFEATHERS

a b s t r a c t

Carpooling is an emerging alternative transportation mode that is eco-friendly and sustain-able as it enables commuters to save time, travel resource, reduce emission and traffic con-gestion. The procedure of carpooling consists of a number of steps namely; (i) create amotive to carpool, (ii) communicate this motive with other agents, (iii) negotiate a planwith the interested agents, (iv) execute the agreed plans, and (v) provide a feedback toall concerned agents. In this paper, we present a conceptual design of an agent-basedmodel (ABM) for the carpooling a that serves as a proof of concept. Our model for thecarpooling application is a computational model that is used for simulating the interactionsof autonomous agents and to analyze the effects of change in factors related to the infra-structure, behavior and cost. In our carpooling application, we use agent profiles and socialnetworks to initiate our agent communication model and then employ a route matchingalgorithm, and a utility function to trigger the negotiation process between agents. Wedeveloped a prototype of our agent-based carpooling application based on the work pre-sented in this paper and carried out a validation study of our results with real data col-lected in Flanders, Belgium.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Nowadays, carpooling is an emerging transportation mode that is eco-friendly and sustainable as it enables commutersnot only to save the travel cost, such as fuel, toll and parking costs, of the carpooling participants, but also to reduce emis-sions and traffic congestions. Carpooling, known as ride-sharing, is the sharing of a car between people (agents) from a cer-tain origin to a specific destination. Thus, in order to study the carpooling concept, we should take into account theinteractions of two or more agents throughout the carpooling process. The procedure of carpooling consists of a numberof steps, namely: (i) create a motive to carpool, (ii) communicate this motive to other agents, (iii) negotiate a plan withthe interested agents, (iv) execute the agreed plans, and (v) provide a feedback to all concerned agents. Creating a motivemeans that a traveler (agent) may choose to carpool because of the availability of travel resources, time, monetary and routecost constraints.

Moreover, change in some socio-economic factors such as the increase in fuel price, in parking costs, or in the implemen-tation of a new traffic policy, may trigger the initiative to carpool. Once to the decision has been made to carpool, the traveler

84 S. Galland et al. / Transportation Research Part C 45 (2014) 83–98

(agent) will try to find one or more potential partners (agents). First, each individual looks in its social network to find carpo-oling companions. If none can be found, global web-based matching advisors can be used. When a company plans to deploysuch matching advisor software, it shall perform thorough testing because a failing service and wrong advice provision willcause customer loss. Furthermore, the company will be interested to study the transient effects occurring during the initialdeployment stage. Neither this evaluation nor the testing can be performed with the help of real users. Hence, a virtual agentcommunity is built. The agent-based model is used to evaluate the global carpooling advisory software.

The carpool initiating agent will send a request to other interested agents in its vicinity. If one or more agents who receivethis request are willing to carpool, then they begin the negotiation phase. In this phase, these agents will negotiate aboutsharing their travel resources and optimizing total costs and daily schedules. After reaching a compromise, these agentscan do carpooling. Meanwhile, an agent can appraise its partners according to their degrees of faithfulness to the carpooling.We call this degree of faithfulness the agent reputation. This reputation factor can serve as a criterion for the selection of apotential partner for carpooling. An agent-based model (ABM) is a class of computational models for simulating the actionsand interactions of autonomous agents with a view to assessing their effects on the systems as a whole (Ferber, 1999; Niaziand Hussain, 2011). ABM is now widely used for modeling increasingly complex systems (Macal and North, 2005; Cossentinoet al., 2010). Application of ABM is not only limited to the computer science domain. Currently, many research areas such astransportation behavior modeling, need to analyze and understand the complex phenomenon of interactions between dif-ferent entities. While traditional modeling tools cannot catch the complexity, ABM can do it through modeling the interac-tion of autonomous agents and deducing the rules for such a system. We, therefore, in this paper propose an agent-basedinteraction model for the carpooling application.

This paper briefly describes a conceptual design of the carpooling application, initially proposed by Cho et al. (2012),Bellemans et al. (2012), and Galland et al. (2013). It uses an agent-based model on the JANUS platform3 (Galland et al.,2010). A simulation model needs to be created to support the individual behaviors of the participants. The contribution of thispaper is the design and the implementation of an agent-based model upon the JANUS multi-agent platform. This platform permitsto individuals to (i) select the best transport mode according to their characteristics; (ii) maintain a social network; (iii) nego-tiate for carpooling; and (iv) carpool the driver and the passengers of a car.

Section 2 presents some related work to the carpooling concept and ABM. Section 3 explains our ABM for the carpoolingapplication with details of the activities and the roles of the agents, and of the environment. Section 4 gives several imple-mentation notes and experimental results. Section 5 is dedicated to our concluding thoughts and ideas for future work.

2. Background

Research on the carpooling concept is largely separated into two parts: (i) technical studies and (ii) empirical studies. Thefirst ones focus on the development of carpooling support systems with techniques of travel route matching (DeLoach andTiemann, 2012; Massaro et al., 2009). In the second part, the overall trend of carpooling – or of the interrelationship betweenwillingness-to-carpool and the socio-economic attributes of the carpooling participants – is treated in general (Kamar andHorvitz, 2009; Horvitz et al., 2005). The previously mentioned studies are limited, and they do not consider the potentialagent (participants) interactions to perform carpooling.

Most transportation-related applications of ABM are related to vehicle routing, pedestrian-flow simulation or demandmodeling efforts (Bernhardt, 2007). Among these applications two of the more widely known are the ABM simulation plat-forms TRANSIMS and MATSIM. TRANSIMS, developed by Los Alamos Lab, is designed to supply transportation planners withmore delicate information about traffic impacts, energy consumption, land-use planning and emergency evacuation (Smithet al., 1995). MATSIM is also a large-scale agent-based simulator similar to TRANSIMS, but it is different using of XML andquickly run simulation, due to a simplified traffic simulator (Waraich et al., 2009). Those applications only consider thewhole effect of each agent’s action on a system, and cannot handle a detailed agent-to-agent or agent-to-environment coor-dination, communication and negotiation.

According to Odell et al. (2002), ‘‘the environment provides the conditions under which an entity (agent or object) exists.’’The author distinguishes between the physical environment and the communication environment. The physical environmentprovides the laws, rules, constraints and policies that govern and support the physical existence of agents and entities. Thecommunication environment provides (i) the principles and processes that govern and support exchanges of ideas, knowl-edge and information, and (ii) the functions and structures that are commonly deployed to exchange communication, suchas roles, groups and interactions protocols between roles and groups.

Odell et al. (2002) define an agent’s social environment as ‘‘a communication environment in which the agents interact ina coordinated manner.’’ This approach is shared by Ferber et al. (2006), Cossentino et al. (2010), and Galland et al. (2009),who proposed to integrate the environment with organizational models. The JANUS platform (Gaud et al., 2008; Gallandet al., 2010) provides an implementation of the agent-based concepts, and of the Capacity–Role–Interaction–Organizationmetamodel (Cossentino et al., 2010). The JASIM library4 (Galland et al., 2009) provides a model of the physical environmentupon the JANUS platform. In the rest of this paper, the graphical notation is inspired by Cossentino et al. (2010).

3 http://www.janus-project.org.4 http://www.multiagent.fr/Jasim_Platform.

S. Galland et al. / Transportation Research Part C 45 (2014) 83–98 85

3. Carpooling model

The carpooling model is designed to consider the individual behaviors during the carpooling process. This process is com-posed by the five steps described in Section 1. The goal is to simulate how everyone is deciding to carpool, and how thecarpooling process is executed. From the simulation’s results, it is possible to understand the causes why people are carpo-oling in a given area.

An agent is defined as someone who lives in our study area and executes his or her own daily schedule in order to satisfyhis or her needs. A schedule is a combination of a number of trips associated with a number of activities. An agent is a mem-ber of household such as the husband, the wife, the parents or the children. (S)He also is a member of the society such as afriend, a colleague, a neighbor, an employee (or an employer) or a student. In our model, we consider the socio-economicattributes, including age, gender, income, education, relationship (within a family), job, vehicle and driving license owner-ship, as a set of input data.

These schedules and attributes are supplied by FEATHERS (Bellemans et al., 2010), an activity-based traffic-demand model,which is developed by IMOB – Hasselt University Belgium. Activity-based modeling (ActBM) is a technique that predicts thedaily travel agenda (schedule) for each member of a synthetic population. Most ActBM generate predictions for a single day.For each predicted activity, the ActBM specifies the activity type, start time, duration, location as well as the duration andtransportation mode for the trip to reach the activity location. Activity-based models are micro simulators: the behaviorsof the individuals are simulated. This allows investigating the overall effects of traffic demand management policies. FEATH-ERS is an operational activity-based model for the region of Flanders (Belgium); it generates the schedules for a given day ofthe week. The input data from FEATHERS consists of:

� the synthetic population for the study area. This contains socio-economic data (household composition, education level,income category, age category, etc.) describing each individual so that the distributions fit the census data,� an area subdivision into traffic analysis zones (TAZ),� land-use data for each TAZ. This consists of tens of attributes including number of people living in the TAZ for several age

and employment categories, amount of people employed in the TAZ in several economic segments (industry, agriculture,education, distribution, hospitals, etc.),� impedance matrices specifying the travel time and distance between TAZ for off-peak, morning-peak and evening-peak

periods and for several transportation modes (car, slow, public transport),� a set of decision trees trained using large scale (periodic) travel surveys. Those data essentially specify individual behavior

as a function of socio-economic data and partial schedule characteristics.

A schematic overview of the data flows in FEATHERS is given by Fig. 1. The Flemish model is characterized by the follow-ing data:

� Synthetic population size: 6 million people.� Number of TAZ: 2368.� TAZ area (average value): �5 km2.� Number of diaries in survey: �8000.

Fig. 1. Agent-based Model for the Carpooling Application. The central node shows the individual planning to carpool. The left hand part shows the initialdaily plan generation by the FEATHERS activity-based model (see also Fig. 2).

Fig. 2. FEATHERS Data Flows and Problem Size Specification for the Flanders Region. The CHAID process generates a set of decision trees from survey data.SynPopGen creates a synthetic population within the study area. FEATHERS predicts a daily agenda for each synthetic individual.

86 S. Galland et al. / Transportation Research Part C 45 (2014) 83–98

Fig. 2 shows a conceptual overview of FEATHERS in a data flow diagram. OVG5 surveys results are used to establish a set of26 decision trees. Training is done using the CHAID (CHi-squared Automatic Interaction Detection) technique (Kass, 1980). Thedecision process used by the individuals is modeled by applying the decision trees in an order. The population within the studyarea is generated by SynPopGen. That population mimics the real population; a large set of marginal distributions of the real andsynthetic population are closely similar. Land-use data consist of the number of jobs, the number of inhabitants, the number andthe size of the schools, and many other indicators for each of the traffic analysis zones (TAZ). Those data are used to calculate theattraction for each TAZ. Finally, the impedance square matrices give the travel times between TAZ for each hour of the day;those are calculated from the network by loading the road network with the expected traffic.

Agents follow a number of steps, including the goal setting, the scheduling based on a given resource and environment,and the execution of their schedule. These steps may be modeled within an activity diagram, which is shown in Fig. 3. Sixmajor activities are considered:

1. ‘‘Mode selection:’’ the agent is selecting its preferred transport mode.2. ‘‘Matching:’’ the agent is selecting its partners.3. ‘‘Negotiation:’’ the agent is negotiating with its partners for the details of the carpooling.4. ‘‘Driving:’’ each driving agent is simulated on a road network.5. ‘‘Feedbacks:’’ each agent computes the feedback at the end of the day according to the activities of the day.6. ‘‘Environment Updating:’’ each non-carpooling agent registers its mobility behavior in the environment.

The following sections detail the global behavior of an agent and these major activities.

3.1. Mode selection activity

The agent is selecting its preferred transport mode. Here, the FEATHERS data are used to determine the mode choice sto-chastically. If the agent decides to carpool, he goes in Activity 2, otherwise he runs its activity in Activity 6.

3.2. Matching activity

The matching is applied in both local and global exploration phases. In both cases, matching precedes the negotiationphase where final decisions to carpool are taken. A person looks for other individuals to cooperate while executing its peri-odic trip (periodicTripEx): this is called exploration. Local exploration within the private social network (PrivNet) is appliedbefore the global exploration. PrivNet is represented by an organization (Fig. 4) in which each agent is playing a role, andhas a relationship with the other members of the organization. If carpool candidates can be found within an agent’s PrivNet,they will be contacted first (as preferred candidates). Global exploration is applied only in a second stage when no suitablepool was found in PrivNet. In the global exploration phase, the matcher provides advice about which pools an individualshould negotiate with. This corresponds to the use of an online service by which to explore the set of formerly unknowncarpooling candidates. Registration in this service implies first posting some descriptive characteristics such as age, gender,education level, special interests (e.g. music style preferences), job category, and driver license availability. Those qualifiersare used because it is known that continued successful cooperation between people requires a minimal level of similarity.

Two people may do carpooling together if their CP ¼ fL; SR; I;Rg are matching. Location (L) is matching the start locationof the agents. Spatial Relevance (SR) is the match between the paths from the origin to the destination of all interactingagents. Interests (I) and Requirements (R) are matching the interests and the requirements of each agent in their profiles,respectively. These matchings are based upon the similarity models described in the following sections.

5 OVG: ‘‘Onderzoek Verkeers Gedrag’’ means Travel Behaviour Research in Dutch.

Fig. 3. Diagram of the activities of a carpooling agent. The numbered activities (with a gray background) are the major activities described in details in thetext. The others are secondary activities related to the implementation on the JANUS platform.

Fig. 4. Household.

S. Galland et al. / Transportation Research Part C 45 (2014) 83–98 87

3.2.1. Profile similarityThe candidate carpooler specifies a set of NA attribute values: those constitute the candidate’s profile. The model uses the

similarity between two profiles as a predictor (one independent variable) for the logit model. The distance between two attri-bute tuples a0 and a1 having NOA ordinal attributes is the Euclidean distance divided by a scale factor to normalize the dis-tance (map to interval ½0;1�) as described by Eq. (1).

dða0; a1Þ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPi2½1;NOA

ða0½i� � a1½i�Þ2

NOA

sð1Þ

Continuous variables are combined into a single distance value dC , and discrete ordinal values are combined into another onedD. The range of dD is a finite subset of ½0;1�. The similarity values sC ¼ ð1� dCÞ; sD ¼ ð1� dDÞ and sE ¼ ð1� dEÞ are used asindependent variables for the logit estimator.

3.2.2. Path similarityThe Global CarPooling Matching Service (GCPMS) per hypothesis has no information about carpool parking, potentially

being used (because that is not specified by the candidates). Therefore, it is assumed that people board and alight at homeand work locations only. The periodic trip executions need to be matched, not people. A periodic trip on Wednesday from Ato be leaving at about 08:30 h needs to be matched with an another one having similar characteristics. Of course, the peopleinvolved shall be mutually compatible but they are not the primary subject of matching. A particular individual can period-ically carpool with several people for different trips in the week (on Monday with colleague A, on Tuesday with neighbor Bwho differs from A). The owner of the first Periodic Trip Execution, abbreviated by periodicTripEx, is the driver.

Let:

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� Oi;Di: denote respectively the origin and destination locations for individual i (e.g. home and work locations);� rða; b; tÞ: denote the route from a to b when starting at time t that is optimal with respect to some cost function cðrÞ based

on distance and travel time;� dðr; tÞ: denote the duration to travel the route r starting at time t;� lðr; tÞ: denote the length to travel the route r starting at time t;� cðrÞ: denote a cost function based on route length lðr; tÞ and route travel duration dðr; tÞ;� pi;soloðOi;Di; tÞ: denote the optimal path from Oi to Di when individual i drives alone (solo) and starts at time t;� pi;soloðOi;Di; tÞ] denote the optimal path from Oi to Di when individual i drives alone (solo) and ends at time t;� pi;carpoolðOi;Di; tÞ: denote the optimal path from Oi to Di when individual i drives the carpool trip via Oj and Dj for i – j and

starts at time t;� pi;carpoolðOi;Di; tÞ: denote the optimal path from Oi to Di when individual i drives the carpool trip via Oj and Dj for i – j and

ends at time t;� pathSimdðÞ: denote the path similarity function for the case where the earliest departure is given;� pathSimaðÞ: denote the path similarity function for the case where the latest arrival is given.

The ratio between the lengths of the optimal routes for the driver is used as a path similarity function. For the given earliestdeparture case (starting at t0) where A is the driver, and the trip is OA ! OB ! DB ! DA, this leads to Eq. (4).

t1 ¼ t0 þ dðrðOA;OB; t0ÞÞ ð2Þt2 ¼ t1 þ dðrðDB;DA; t1ÞÞ ð3Þ

pathSimdðpteA; pteB; cðÞÞ ¼cðOA;DA; t0Þ

cðOA;OB; t0Þ þ cðOB;DB; t1Þ þ cðDB;DA; t2Þð4Þ

Note that t1 denotes the time at which the carpool trip leaves OBn and t2 denotes the time at which the carpool trip leavesDB. Moreover, the Inequalities 5 and 6 hold since the departure times can differ.

pathSimdðpteA; pteB; cðÞÞ – pathSimaðpteA; pteB; cðÞÞ ð5ÞpathSimaðpteA; pteB; cðÞÞ – pathSimaðpteB; pteA; cðÞÞ ð6Þ

The departure time can have a large effect upon the trip duration. In the first GCPMS, this dependency is ignored due tolack of data. Because of the availability of speed profiles registered using GPS navigators, it will become feasible to take thetime dependency into account (which will lead to more accurate negotiation outcome prediction) in the near future althoughthat will require a large amount of data pre-processing and data storage. By ignoring time dependency, Eq. (4) is reduced toobtain the Eq. (7).

pathSimdðpteA; pteB; cðÞÞ ¼cðOA;DAÞ

cðOA;OBÞ þ cðOB;DBÞ þ cðDB;DAÞð7Þ

3.2.3. Time interval similarity evaluation for matchingIt is not feasible to ask the individuals to register the piecewise linear preference function mentioned in Section 3.3.2.

People are assumed to be prepared to register simply a time interval only. Hence the preference value is assumed to be aconstant f over the time interval specified.

The negotiation outcome is assumed to be positively correlated to the intersection’s length of the intervals associatedwith the periodicTripExs to compare. The time interval similarity tis is given by the equations:

t0 ¼maxðtiA ;0; tB;0Þ ð8Þt1 ¼minðtiA ;1; tB;1Þ ð9ÞtisðiA; iBÞ ¼ t1 � t0 ð10Þ

For a given pair of periodicTripExs, tis values are fed into the logit estimator as two independent variables; combining theminto a single value would cause a loss of information.

3.2.4. Reputation of the agentsEach driver has a safety reputation value (sReputation) that evolves over time due to the qualifications by the passengers.

They are the individuals who participated in an agreement in which the person being evaluated is the driver.Each person (both drivers and passengers) has a timeliness reputation (tReputation). This qualifies the individual as being

on time to start the trip (not wasting someone else’s time).Both reputation values are handled in the same way. Details are explained here for the sReputation case. The most-recent

qualification is saved by each issuer. The sReputation is calculated as a weighted average of the values in the list of all thequalifications: the weight decreases with the age of the qualification, and increases with the duration of the cooperationa:durðn:tsðÞÞ up to the moment of the qualification (the agreement lifetime). Let Qi0 be the qualifications list for individual

S. Galland et al. / Transportation Research Part C 45 (2014) 83–98 89

i0. Let ai0j denote an agreement in which individuals i0 and j cooperated. Let a:issðÞ denote issuer of the qualification. n:tsðÞ

denotes the time at which the qualification was issued and a:durðtÞ denotes the lifetime of agreement at a time t. Then

age ¼ now� n:tsðÞ ð11Þwi0

n:issðÞ ¼ expð�a � ageÞ � ai0n:issðÞ:durðn:tsðÞÞ ð12Þ

sReputationi0 ¼

Xn2Qi0

n:sRepðÞ �wi0n:issðÞ

Xn2Qi0

wi0n:issðÞ

ð13Þ

Every agent keeps a list containing a perceived safety reputation value for a limited set of other agents. In the exerciser, aspecific agent can be qualified by zero or more safety reputation values (each one of which is owned by a peer). Every agentcan determine the reputation of another agent using a method that is not specified in this section and overriding the valuealready in place (if any). Furthermore, everyone can adjust the reputation of peers based on gossip as follows. At a randommoment in time, an emitter agent ae can multicast its reputation value ReðqÞ to qualify agent aq to a subset of agents directlyconnected to it in the social network. The receiver ar:1. retransmits the reputation message with a given probability pr (hence simply drops it with probability ð1� prÞ),2. adjusts its own perception of aq with a given probability pa (hence simply ignores it with probability ð1� paÞ).

Consider agents ae; aq; ar; av that are all pair wise different. ae emits a qualification about aq that reaches ar via its neighborav . If ar has not yet registered an opinion about aq, the value for RrðqÞ is 0. Reputation update by receiver aa is done by:

a ¼ 2�dðe;rÞ ð14Þbr;v 2 ½0;1� ð15Þ

R0rq RrðqÞ þ a � b � ReðqÞ

1þ a � br;vð16Þ

where dðe; rÞ is the distance between emitter and receiver in the network and br;v is the strength of the link between ar and av .

3.3. Negotiation activity

The negotiation is the process during which the members of a pool are negotiating the details of their periodicTripExs (timewindow, who is the driver and the passengers).

3.3.1. Overview of the negotiation activityIf the negotiation fails, the agent goes back to Activity 1; otherwise to Activity 4. The negotiation is based on a specific

protocol. According to our organizational approach, the agents who are negotiating together are members of the same orga-nization ‘‘Negotiation Pool’’ (Fig. 5). The negotiation protocol is described as a sequence of messages exchanged by the dif-ferent participants, as illustrated by Fig. 7. This negotiation protocol is re-launched when new time windows are proposed,and until all the participants were found (success of the negotiation), or when the initiator of the negotiation is consideringthat it is impossible to obtain a common decision among the participants (failure of the negotiation).

If an individual joins a pool, (s)he is added to the PrivNet for all other participants in the pool (if still required), so that if i0

and i1 cooperate in a pool, ði0; i1Þ and ði1; i0Þ belong to each other’s private networks. Because the links are never removedfrom the PrivNet, if i0 and i1 ever carpooled, ði1Þ 2 PrivNetði0;1Þ ^ ði0Þ 2 PrivNetði1;1Þ. Candidates register, join and leavethe pools at random moments in time. As a consequence, the main data structures dynamically change due to events externalto the matching process.

Fig. 5. Negotiation pool.

Fig. 6. Trip pool.

Fig. 7. Sequence diagram of the negotiation protocol.

90 S. Galland et al. / Transportation Research Part C 45 (2014) 83–98

The negotiation process is a discrete variable with the outcome value success (yes) or failure (no). A logit model is used topredict the negotiation outcome. Negotiation results fed back to the Global CarPooling Matching Service (GCPMS) are used todetermine the coefficients in the logit model by linear regression.

After having found a good match, the matcher conveys its advice to the involved candidates (the owners of the matchedperiodicTripEx). They evaluate the proposal, negotiate about carpooling and possibly agree to cooperate. It is impossible topredict the negotiation phase with certainty; reasons are:

1. Negotiation covers the driver’s selection, the co-route determination, and the re-scheduling (daily planning adaptation)for the cooperators. Schedule adaptation makes use of VOT (individual specific Value Of Time). An advisory mechanismdoes not have all required data available nor has any knowledge of the private goals (and in general, the beliefs, desires,intentions – BDI) of the individuals (agents) involved in a negotiation.

2. The total distance driven cannot be predicted by the matcher when carpool parking is involved, because in such a case, theco-route can be tree structured. Hence the path similarity function delivers only an approximation of the one involved innegotiation.

S. Galland et al. / Transportation Research Part C 45 (2014) 83–98 91

3. People are assumed to be prepared posting a minimal amount of data about the time intervals that suit them for depar-ture an arrival respectively; candidates are supposed to specify just the interval boundaries. However, during negotiation,they can make use of preferences to state that one of a set of proposed intervals suits better than another one. Hence, thetrip times interval similarity function available to the matcher is only an approximation for the one used duringnegotiation.

4. The Cotravel_Refused allows individuals to avoid unconditionally any advice to carpool with specific people. For privacyreasons, it is impossible for a refused individual to know the refusing party.

Therefore, the candidates convey the negotiation result back to the matcher service. This paper assumes that sufficient(financial) incentives are in place in order to make this happen. The feedback is used by a learning mechanism incorporatedinto the matching service. After receiving the feedback, the matching service disposes of the periodicTripEx and the individ-uals’ characteristics as well as of the negotiation result; those are used to train a predictor.

3.3.2. Time interval based functions for negotiationThe departure (resp. arrival) interval for a trip (periodicTripEx) is the time interval that suits the traveler to start (resp. end)

the trip. Let pte:idðÞ and pte:iaðÞ denote respectively the departure and arrival intervals of the periodicTripEx pte.The preference of the individual p0 for a given moment in time is provided by the function fp0

: R) R : t # f p0ðtÞ 2 ½0;1�.

The function is not required to be differentiable or continuous, but it shall be integrable. For each moment in time belongingto the departure and arrival intervals, the preference value needs to be specified.

The combined preference function is the product of the preference functions associated with two periodicTripExs. It isessential to the negotiation process.

The integral of the combined preference over a fixed time interval in ½0;1Þ is called the time interval suitability. The lengthof the interval has a pre-specified constant C value. A suitable choice is the expected duration of the trip interruption to getsomeone in or outside of the vehicle. The time interval suitability is denoted by SðC; iA; fA; iB; fBÞ, where iA ¼ ½tiA ;0; tiA ;1� andiB ¼ ½tiB ;0; tiB ;1� are the intervals specified by the individuals A and B; fA and fB are the associated preference functions. The suit-ability function is given by the following equations:

t0 ¼maxðtiA ;0; tiB ;0Þ ð17Þt1 ¼minðtiA ;1; tiB ;1Þ ð18Þ

Sðt; C; iA; iB; fA; fBÞ ¼R tþC

t fAðxÞ � fBðxÞdx if t 2 ½t0; t1 � C�0 otherwise

(ð19Þ

where t denotes the start of the boarding/alighting operation. The dimension of the combined time interval suitability value is½prefUnit2

; timeUnit�. In this context, preference is assumed to be dimensionless hence the suitability dimension reduces to½timeUnit�. During negotiation, Sðt; C; iA; iB; fA; fBÞ is with other functions to find a suitable time to board/alight.

Piecewise linear functions are used because they are flexible. They can easily be specified by the user (responsible for theconfiguration of the agent-based model), and their integration is computationally cheap. The left hand part in Fig. 8 showspiecewise linear preference functions, their product and the associated time interval suitability (crosshatched area under theproduct function). The right hand part shows the case for the same intervals where the preference function is assumed toequal one everywhere: this is the assumption made by the matching service due to lack of information: the user only spec-ifies the boundaries for the departure and arrival intervals.

3.3.3. Agreement attributesIn this section we will present the three basic attributes important for constituting an agreement between agents.

� Cohesion of an Agreement; Cohesion is supposed to be a monotonically decreasing function of the time t, which is elapsedsince the creation of the agreement. Cohesion is a monotonically decreasing function of the pool size s (large pools are morelikely to disintegrate). The cohesion does not depend on mutual evaluation of carpoolers. The cohesion and the reputationshall be independent concepts. Indeed, they are fed into a probability estimator. The cohesion value is given by:

c ¼ ea�t � eb�ðs�1Þ ð20Þ

In the pair wise case, when considering a specific edge, exactly two cohesion values apply (one for each of the vertices (peri-odicTripExs)). Each of the cohesion values possibly applies to an agreement. For a given pair of periodicTripExs ðpte0; pte1Þ, thec0 and c1 can relate to either different agreements or to a single one. The meaning of the tuple ðc0; c1Þ depends on the numberof agreements involved. Therefore, cohesion values are combined into a single cohesion based indicator using the function gi-ven in Eq. (22). The second case in Eq. (22) is for when both periodicTripExs are members of an agreement (but not necessarilyto the same one). Let pte0; pte1 2 T the periodicTripExs involved. Let c0 and c1 denote the respective corresponding cohesionvalues, and p:TðÞ denotes the list of the periodicTripExs that are involved in the pool p. Let pte:aðÞ denotes the agreement cov-ering pte when it belongs to a pool. The cohesion indicator cðpte0; pte1Þ is a measure for the cohesion between two periodic-TripExs, when they already form a pair, and for the feasibility to get them released when they are bound in pairs with others.

Fig. 8. (Left) Time similarity used while negotiating: fA;NðtÞ and fB;NðtÞ are time preference functions for specific intervals. FNðtÞ is the combined preferenceand the size of the cross-hatched area is the resulting time interval suitability function. (Right) Time similarity used by the matcher: all preference functionsequal 1 because users are expected to only submit feasible time intervals.

92 S. Galland et al. / Transportation Research Part C 45 (2014) 83–98

ptex:aðÞ ¼nil if 9= p 2 Pjptex 2 p:TðÞp:aðÞ if 9p 2 Pjptex 2 p:TðÞ

�ð21Þ

cx ¼0 if ptex:aðÞ ¼ nil

ptex:aðÞ:cðÞ else

�ð22Þ

c ¼ð1� c0Þ � ð1� c1Þ if pte0:aðÞ– pte1:aðÞc0 � c1 if pte0:aðÞ ¼ pte1:aðÞ– nil

�ð23Þ

In the case that both periodicTripExs belong to the same agreement, the cohesion values are taken from that agreement, and infact c0 ¼ c1. In the other case (which also covers the case where at least one of the periodicTripEx is not covered by an agree-ment), the complement of the cohesion values is used. When neither of the periodicTripEx belongs to an agreement, c ¼ 1.� Safety Reputation: While evaluating the success probability for a pool, exactly one sReputation value applies since only the

sReputation for the driver is relevant.� Timeliness Reputation; The tReputation of an individual i0 applies to an agreement, and exists only exists as long as the

agreement holds. It can only be affected by the partners in the agreement that are different from i0 (in the pair wise case,there is only one such partner). The tReputation is an evaluation score assigned by the partners.

3.4. Driving activity

The driving activity corresponds to the execution of the trip. The driver controls its car (with the carpooled passengersinside) on the roads. The road network is represented by a graph built from geographic data. The JANUS platformprovides an environment model able to support the displacements of the cars on the roads (Galland et al., 2009). Fig. 6 pre-sents the organization that is supporting the trip simulation. All the agents in a trip pool must play a role in an instance ofthis organization. The behavior of the Driver role is composed of two layers: (i) the path planning on the roads and (ii) thepath following and collision avoidance.

S. Galland et al. / Transportation Research Part C 45 (2014) 83–98 93

Algorithm 1. Behavior of the driving agents

1: function DRIVER BEHAVIOR

2: repeat3: path hsi:ej8s0 2 b; path ¼ b:hsi:e ^ position 2 s ^ position R s0f g4: if :is FreePathpath then5: g firstJunctionInpath6: if g then7: p astarposition; g8: path hsi:ej8s0 2 b; path ¼ b:hsi:e ^ g 2 s ^ g R s0f g9: path p:path10: else11: path astarposition; goal12: end if13: end if14: p getPerceivedObjectspath; roads15: update AttributesAccordingTop16: o faj8b 2 p; distanceposition; b P distanceposition; ag17: if o18: a raðfollowerDrivingo; acceleration; speed; positionÞ19: else20: a raðfreeDrivingacceleration; speed; positionÞ21: end if22: speed rsðspeedþ a:Dt

2 Þ23: position positionþ speed:Dt24: if speed > 0 then25: waitingTime 026: else27: waitingTime waitingTimeþ Dt28: end if29: until position ¼ goal30: end function31: function ISFREEPATH(path)32: return path – hi ^ :path½1�:isBlocked ^waitingTime < timeout33: end function34: function FIRSTJUNCTIONIN(path)35: r nil36: for all ha; bi 2 path ^ : r37: c fiji 2 a ^ i 2 bg38: if kneightborðcÞkP 3 then39: r c40: end if41: end for42: return r43: end function

The behavior of the agents, who are driving during the simulation, is described by Algorithm 1. Every agent maintains asequence of connected road segments6 to follow on the road network, says the path:

6 hai7 a:b is

path ¼ hsiji 2 ½0; nÞ^ ð24Þsi \ si�1 – ; ) i > 0^si \ siþ1 – ; ) i < ni

Initially, the path is the shortest path between the position of the agent and its goal (given by the function ASTAR in Algo-rithm 2). At every simulation-time step, the roads already traveled are removed from the path (line 3 of Algorithm 1).7

is the sequence of road segments such that, 8a 2 a; a is a road segment.the sequence of road segments starting by the sequence a and finishing by the sequence b.

94 S. Galland et al. / Transportation Research Part C 45 (2014) 83–98

Algorithm 2. The A⁄ algorithm

1: function ASTARðstart; goalÞ2: closeset ;3: openset fstartg4: came from½start� nil5: g½start� 06: f ½start� g½start� þ hðstart; goalÞ7: while openset do8: c sj8ðm; sÞ 2 openset2; f ½s� 6 f ½m�

� �9: if c ¼ goal10: p hi11: while goal do12: p hsegmentcame from½goal�; goali:p13: goal came from½goal�14: end while15: return p16: end if17: openset openset � fcg18: closeset closeset [ fcg19: for all n 2 neightborðcÞ do20: ng g½c� þ distanceðc;nÞ21: if n R openset _ ng < g½n� then22: came from½n� c23: g½n� ng24: f ½n� g½n� þ hðn; goalÞ25: openset openset [ fng26: end if27: end for28: end while29: return hi30: end function

The path planning is dynamic: the driver adapts its path according to its perceptions from the environment jams, road-works with a variant of the A⁄ search algorithm (Dechter and Pearl, 1985; Delling et al., 2009), with its principles closed tothe D⁄-Lite algorithm (Koenig and Likhachev, 2005). This family of path-planning algorithms has two advantages: it en-ables path re-computation during the simulation according to a new state of the environment; and it is suitable for a par-tial knowledge of the environment’s state. Lines 4–13 provide the behavior for the dynamic re-planning of the path. Thefunction ISFREEPATH determines if the following segments along the path are traversable. If they are not, the segments to thesubsequent junction along the path are replaced by the shortest path from the current position to this junction. If there isno junction on the path, it becomes the shortest path to the goal. The A⁄ search algorithm is used to compute all the short-est paths. It is described in Algorithm 2. A⁄ uses a best-first search and finds a least-cost path from a given initial road toone goal segment. As A⁄ traverses the graph of the roads, it follows a path of the lowest expected total cost or distance,keeping a sorted priority queue of alternate path segments along the way. It uses two base functions: (i) the past path-costfunction gðxÞ, which is the known distance from the starting segment to the current segment x, and (ii) a future path-costfunction hðxÞ, which is an estimation of the distance from x to the goal. The function hðxÞ must be an admissible heuristic;that is, it must not overestimate the distance toward the goal. Thus, for an application like routing, hðxÞ might representthe straight-line distance to the goal, since that is physically the smallest possible distance between any two points ornodes.

After the driving agent has updated its path, he follows it, and he avoids collisions with the other cars around. The func-tion GETPERCEIVEDOBJECTS at line 14 is provided by the JASIM library, and it replies the set of objects in the field-of-perception ofthe driver. A standard Intelligent Driver Model (Treiber et al., 2000) is used at line 18 to adapt the velocity of the car accord-ing to the ahead vehicles and to the road signs: the traffic lights and stop signs are assimilated to immobile vehicles until thedriver decided to pass through. The other road signs are used to update the variables in the driving model (desired velocity).The acceleration is defined by Eq. (25), where Dv is the difference between the velocities of the agent and the ahead object.Dp is the distance to this ahead object. b is the comfortable braking deceleration. s is the security distance, and w is the de-sired time headway to the vehicle in front.

S. Galland et al. / Transportation Research Part C 45 (2014) 83–98 95

followerDriving ¼� vDvð Þ2

4bDp2 if the ahead object is far

�a sþvwð Þ2Dp2 if the ahead object is near

8<: ð25Þ

On a free road, the vehicle is asymptotically approaching its desired velocity. The corresponding acceleration is defined byEq. (26), where a is the current acceleration, v is the current velocity, and vc is the desired velocity.

freeDriving ¼ a 1� vvc

� �4 !

ð26Þ

In Algorithm 1, the functions raðxÞ and rsðxÞ ensure that the computed acceleration and speed (given as parameters) are in-side the ranges allowed by the physic description of the vehicle. After the pool’s vehicle has reached its goal, all the agents ofthe pool execute Activity 5.

3.5. Feedback activity

Feedbacks are computed at the end of the day according to the activities during the day, and are given to the carpoolers.This activity is the last of the day for a carpooling agent.

3.6. Environment updating activity

The environment updating is the activity that permits to a non-carpooling agent to register its mobility behavior in theenvironment in order to influence the driving simulation of the carpooler agents. Individual vehicles may be generated in themicroscopic simulation model used in Activity 4. This activity is the last of the day for a non-carpooling agent.

4. Experimental results and implementation discussion

Experimentations were done on a population of 1000 people. One of the major goals of our experimentation is to computeand possibly optimize the solution time required to compute the (complex) agent-based interactions between people(nodes). One reason for doing this is to be able to replay reality and accurately predict carpooling negotiation outcome inorder to dispose of a sufficient synthetic population to exercise a global carpooling matching advisor software. The tripsare extracted from the data into the FEATHERS framework. The considered region is Flanders, Belgium. Fig. 9 illustratesthe simulator windows: the lower-left window shows the roads, and the upper-left window displays the parameters ofthe simulation.

Fig. 9. Screenshot of the simulator.

96 S. Galland et al. / Transportation Research Part C 45 (2014) 83–98

The first experimentation is the proportion of drivers and passengers for every quarter of hours during the reference day.Fig. 10 gives the histograms for each category. 2/3 of the population are driving; 1/3 of the population is composed of pas-sengers. The results obtained using our agent-based simulations are very interesting as they are close to reality, which can becompared with the original data extracted using the FEATHERS framework. Indeed, during the negotiation process, the poolpartners do not change the time window of their trips.

Fig. 11 gives the histograms for the distribution among the transport modes for every quarter of hours during the refer-ence day. 65% of the people are traveling in single vehicles; 31% are using the public transports; and 4% are carpooling. Theaverage number of people per carpooling pool is of 2 with standard deviation of 1. The traffic density is still high during thehigh-activity periods: during the negotiation, the partners are not accepting enough changes in the time window of theirtrips. Therefore, they prefer to select the single-vehicle or the public transport modes than carpooling.

Fig. 12 gives the average computational times for the simulation of a day on an Intel Core i7 CPU 960 at 3.20 GHz, fourcores, with Windows Seven (64 bits). Because the JASIM environment model is based upon the Influence-Reaction model (Mi-chel, 2007), which permits to handle and solve the conflicts among simultaneous actions, the scheduling of the agents is astandard loop (each loop represents two seconds during the day). This approach does not cause a causality problem amongthe agent actions during the simulation. For the first curve, the people who do not want to carpool are also simulated duringthe trip execution. For the second curve, only the carpoolers are simulated.

Our simulator may be improved on several points: (i) the quality of the simulation’s results, and (ii) the global perfor-mance of the simulator. The algorithms deployed in our model are designed according to the simplicity principle, and areeasily replaceable by any other (compatible) negotiation protocols available to the agent-based community. The global

0

5

10

15

20

25

30

35

40

07:00 09:00 11:00 13:00 15:00 17:00 19:00 21:00

Den

sity

DriversPassengers

Fig. 10. Traffic density for each quarter of hours during the reference day, and per people category.

0

5

10

15

20

25

30

35

40

07:00 09:00 11:00 13:00 15:00 17:00 19:00 21:00

Den

sity

Single vehiclePublic transport

Carpooling

Fig. 11. Traffic density for each quarter of hours during the reference day, and per transport mode.

0

200

400

600

800

1000

1 10 100 1000 10000

Com

puta

tion

Tim

e (m

inut

e)

Count of Agents

All people are simulatedOnly carpoolers are simulated

Fig. 12. Average computation time for a day.

S. Galland et al. / Transportation Research Part C 45 (2014) 83–98 97

exploration is skipped in this study because we do not have an online system for carpooling in place currently. We have pre-sented the details of our approach for global exploration earlier in our paper and we intend to work on it as a part of thefuture work. The microscopic simulation of the vehicles may be replaced by a mesoscopic or macroscopic simulation modelto improve the performances of this module. Performance is a crucial issue because the aim of the agent model is to serve asan active synthetic population to exercise the global advisor software. Wall clock time available for testing is limited andlarge agent communities are required for realistic evaluation. Hence, performance issues will get priority focus. In thecase of a microscopic simulation, the agent scheduler used on the JANUS platform may be replaced by an asynchronousscheduler (based on operating-system threads). This solution enables to run groups of agents in parallel in place of thecurrent sequential approach. The current implementation is a proof-of-concept. All the algorithms must be tuned andredesigned to improve their performances. Our model and its implementation reproduces the behavior of a population ina carpooling problem. The microscopic simulation permits to reproduce the trip execution with high level of details (e.g. traf-fic jams).

5. Conclusion

In comparison to the state-of-the-art research work, the work/study presented within this paper has a number ofadvantages. Some of them are (i) the ability to analyze various effects of agent interaction with a detailed view on bothcommunication and negotiation aspects, and (ii) the ability to simulate learning, adaptation and behavior reproductionof agents through modeling their interactions. Our simulation model on the JANUS platform provides a solution to a complexsimulation but needs a lot of computing resources (e.g. processing time, memory, and data storage) because of the highnumber of agents to simulate, and the big data processing for each agent. The agent-based model described constitutesan active synthetic population that can be used to exercise a global matching advisor for carpooling. Such advisor consistsof complex mechanisms, including machine learning. Furthermore, it requires a critical mass of customers to operate effi-ciently. Exercising the advisor is useful for testing and for transient phenomena analysis. Like all models that cover real-world transportation problems, the simulation model proposed in the paper: (i) requires a large amount of detailed andaccurate input data, including agent’s socio-economic attributes and road network information and (ii) has scalabilityissues that are still to be solved. Indeed, it is necessary to consider a sufficiently large region to evaluate the carpoolingprocess. Apart from scalability issues, future research will focus on enhancing the procedure for negotiation betweenagents.

Acknowledgments

Part of this work carried out under the European FP7 Open-FET project Data Science for Simulating the Era of ElectricVehicles (DATASIM) (project number FP7-ICT-270833).

This material is partly based upon the library JASIM, supported by Voxelia SAS. The views and conclusions contained with-in this document are those of the authors, and should not be interpreted as representing the official policies, either expressedor implied, of the Voxelia SAS.

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